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The water tank in the diagram below is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 96 feet.  The water in the tank is 50% of the tank's capacity.  Find the height of the water in the tank.

 

 Nov 27, 2020
 #1
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Volume of water  held  when the tank is full

 

(1/3) pi * radius ^2 * height  =     (1/3) pi  * (16)^2 (96)  = 8192 pi   ft^3

 

When the tank is half- full.....the volume  =   8192 pi / 2   = 4096 pi ft^3

 

Using  silimlae triangles  we  have  that

 

r / h =  16 / 96 

 

r /  h =     1/6

 

r =   h/6

 

So.......we have  that

 

4096 pi  = (1/3) pi  r^2  h        subbing for  r  we have that

 

4096 pi  = (1/3) pi ( h/6)^2 * h        simplify

 

4096 = (1/3) h^3 / 36

 

4096 =  h^3  / 108

 

108 * 4096  = h^3

 

442368  = h^3        take the cube root of both sides

 

h ≈  76.2  ft

 

 

cool cool cool

 Nov 27, 2020

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